1. Field of the Invention
This patent specification relates to chromatography. More particularly, this patent specification relates to systems and methods for separations of compounds during chromatographic analysis.
2. Background of the Invention
Chromatography is an area of analytical chemistry focused on the separation of complex mixtures of gases, liquids, and/or solids in an attempt to analyze the sample by identifying and/or quantifying various components of the mixture. Chromatography is classically performed with columns of fixed geometry, either in an open tubular or packed design. A stationary phase is deposited on the inner surfaces of the column, either on the inside walls in the case of the open tubular design, or on the packed particles for a packed design. In some cases the packed particles and stationary phase are one and the same. Such configurations are usually packaged as tubes that can be connected in various ways to chromatographic equipment.
Traditional chromatographic separations are accomplished through differential migration. The partitioning of analyte species between a mobile phase and a stationary phase results in each analyte band migrating along the separation column at a unique velocity that is less than that of the mobile phase. This velocity is determined by the magnitude of the partition coefficient, the phase ratio (ratio of volumes of stationary and mobile phases), and the velocity of the mobile phase (un-retained species). The time spent in the mobile phase determines the degree to which analytes are retained. Although these factors can change slightly down the length of the column due to a variety of factors, band velocity is conventionally considered to be relatively constant throughout a separation under isothermal conditions with a constant flow rate and composition of mobile phase. As a result of differential migration, bands of analytes can be physically separated as long as the rates of differential migration vary by a large-enough factor.
However, there remains a general problem with conventional chromatography approaches due to a phenomenon known as band broadening. Band broadening is the tendency for bands on a chromatographic column to continuously grow longer due to a variety of sources which are primarily related to diffusion. In general, longitudinal diffusion is a dominating factor, and is proportional to the square-root of time spent on the column. Since differential migration results in a linear increase in band-to-band distances (measured center to center) as a function of time, and band broadening decreases the band-to-band distance (measured edge to edge) with the square-root of time, the chromatographic resolution is usually generalized to be proportional to the square-root of time spent on the column. FIGS. 1a-1d illustrate the effects of differential migration and broadening on chromatographic resolution, according to conventional chromatography techniques. FIG. 1a shows two components, “A” and “B,” in FIGS. 1a-c for simulated uniformly wall-coated tubular column having infinite length. FIG. 1a is a band trajectory plot where the differential migration is apparent. FIG. 1b shows band broadening as a function of time. FIG. 1c shows velocity as a function of time. FIG. 1d shows the calculated resolution between bands A and B as a function of time. In FIG. 1d, chromatographic resolution is calculated for each “vertical slice” of the plots in figure A, that is the difference in band position divided by the average band width. Note that this measure of resolution is not the same as that typically observed on a chromatographic system with a column of finite-length and a detector that is after the column. The type of separation illustrated in FIGS. 1a-d is essentially a situation of “diminishing returns” where the chromatographer can not improve the chromatographic resolution in a time-effective manner by using a longer column. In an effort to improve band separations in a more time-effective manner, conventional chromatographic techniques have focused on optimizing column diameters, mobile phase flow rates, stationary phase functionality and thickness, and other factors.